Which of the following numbers is a multiple of 6? ${56,68,77,78,116}$
The multiples of $6$ are $6$ $12$ $18$ $24$ ..... In general, any number that leaves no remainder when divided by $6$ is considered a multiple of $6$ We can start by dividing each of our answer choices by $6$ $56 \div 6 = 9\text{ R }2$ $68 \div 6 = 11\text{ R }2$ $77 \div 6 = 12\text{ R }5$ $78 \div 6 = 13$ $116 \div 6 = 19\text{ R }2$ The only answer choice that leaves no remainder after the division is $78$ $ 13$ $6$ $78$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $78$ $78 = 2\times3\times13 6 = 2\times3$ Therefore the only multiple of $6$ out of our choices is $78$. We can say that $78$ is divisible by $6$.